The 25-year-old was born in Manchester, but qualifies for Poland through his grandfather.
"I've always seen myself as an English person so to play for Poland would be difficult," Tarkowski told reporters.
"I know that side of the family, it's not something I've never thought of or people I've never spoken to, but I've always seen myself as English. It's only really the name that's followed me around.
"There were a couple of conversations with people not at the top of the Polish FA but a couple of people associated with them, mentioning would I think about it and would I look at it? At times, throughout my career, I've thought about it but I always saw myself as English so that was the most important thing."
Tarkowski could make his England debut in Friday's international friendly with the Netherlands.